Critical Bending Moment for Simply Supported Open Section Beam Formula

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The Critical Bending Moment is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation. Check FAQs

M cr = (\frac{π}{L}) \cdot \sqrt{E \cdot I y \cdot ((G \cdot J) + E \cdot C w \cdot (\frac{π^{2}}{{(L)}^{2}}))}

M_cr - Critical Bending Moment?L - Unbraced Length of Member?E - Modulus of Elasticity?I_y - Moment of Inertia about Minor Axis?G - Shear Modulus of Elasticity?J - Torsional Constant?C_w - Warping Constant?π - Archimedes' constant?

Critical Bending Moment for Simply Supported Open Section Beam Example

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Here is how the Critical Bending Moment for Simply Supported Open Section Beam equation looks like with Values.

Here is how the Critical Bending Moment for Simply Supported Open Section Beam equation looks like with Units.

Here is how the Critical Bending Moment for Simply Supported Open Section Beam equation looks like.

9.8021 = (\frac{3.1416}{10.04}) \cdot \sqrt{10.01 \cdot 10.001 \cdot ((100.002 \cdot 10.0001) + 10.01 \cdot 10.0005 \cdot (\frac{{3.1416}^{2}}{{(10.04)}^{2}}))}

9.8021N*m = (\frac{3.1416}{10.04cm}) \cdot \sqrt{10.01MPa \cdot 10.001kg·m² \cdot ((100.002N/m² \cdot 10.0001) + 10.01MPa \cdot 10.0005kg·m² \cdot (\frac{{3.1416}^{2}}{{(10.04cm)}^{2}}))}

9.8021 = (\frac{3.1416}{10.04}) \cdot \sqrt{10.01 \cdot 10.001 \cdot ((100.002 \cdot 10.0001) + 10.01 \cdot 10.0005 \cdot (\frac{{3.1416}^{2}}{{(10.04)}^{2}}))}

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Critical Bending Moment for Simply Supported Open Section Beam Solution

Follow our step by step solution on how to calculate Critical Bending Moment for Simply Supported Open Section Beam?

FIRST Step Consider the formula

M cr = (\frac{π}{L}) \cdot \sqrt{E \cdot I y \cdot ((G \cdot J) + E \cdot C w \cdot (\frac{π^{2}}{{(L)}^{2}}))}

Next Step Substitute values of Variables

∴

M cr = (\frac{π}{10.04cm}) \cdot \sqrt{10.01MPa \cdot 10.001kg·m² \cdot ((100.002N/m² \cdot 10.0001) + 10.01MPa \cdot 10.0005kg·m² \cdot (\frac{π^{2}}{{(10.04cm)}^{2}}))}

Next Step Substitute values of Constants

∴

M cr = (\frac{3.1416}{10.04cm}) \cdot \sqrt{10.01MPa \cdot 10.001kg·m² \cdot ((100.002N/m² \cdot 10.0001) + 10.01MPa \cdot 10.0005kg·m² \cdot (\frac{{3.1416}^{2}}{{(10.04cm)}^{2}}))}

Next Step Convert Units

∴

M cr = (\frac{3.1416}{10.04cm}) \cdot \sqrt{10.01MPa \cdot 10.001kg·m² \cdot ((0.0001MPa \cdot 10.0001) + 10.01MPa \cdot 10.0005kg·m² \cdot (\frac{{3.1416}^{2}}{{(10.04cm)}^{2}}))}

Next Step Prepare to Evaluate

∴

M cr = (\frac{3.1416}{10.04}) \cdot \sqrt{10.01 \cdot 10.001 \cdot ((0.0001 \cdot 10.0001) + 10.01 \cdot 10.0005 \cdot (\frac{{3.1416}^{2}}{{(10.04)}^{2}}))}

Next Step Evaluate

∴

M cr = 9.80214499156555N*m

LAST Step Rounding Answer

∴

M cr = 9.8021N*m

Critical Bending Moment for Simply Supported Open Section Beam Formula Elements

Variables

Constants

Functions

Critical Bending Moment

The Critical Bending Moment is crucial in the proper design of bent beams susceptible to LTB, as it allows for slenderness calculation.

Symbol: M_cr

Measurement: Moment of ForceUnit: N*m